Quantum state geometry and entanglement of two spins with anisotropic interaction in evolution
Abstract
Quantum evolution of a twospin system with anisotropic Heisenberg Hamiltonian in the magnetic field is considered. We show that this evolution happens on some manifold with geometry depending on the ratio between the interaction couplings and on the initial state. The FubiniStudy metric of this manifold is calculated. The entanglement of the states belonging to this manifold is examined. Also we investigate similar problem for a twospin system described by the DzyaloshinskyMoria Hamiltonian. The problem is solved by using the fact that this Hamiltonian and the anisotropic Heisenberg Hamiltonian are linked by the unitary transformation.
 Publication:

Journal of Geometry and Physics
 Pub Date:
 June 2017
 DOI:
 10.1016/j.geomphys.2017.01.021
 arXiv:
 arXiv:1605.01590
 Bibcode:
 2017JGP...116...81K
 Keywords:

 Quantum evolution;
 Manifold;
 FubiniStudy metric;
 Entanglement;
 Quantum Physics;
 Mathematical Physics
 EPrint:
 16 pages, 2 figures